A Village Has Five Residents, Each of Whom Has an Accumulated

Multiple Choice

A village has five residents, each of whom has an accumulated savings of $50. Each villager can use the money to buy a government bond that pays 10% interest per year or to buy a year-old goat, send it onto the commons to graze, and sell it after one year. The price of the goat that the villager will get at the end of the year depends on the amount of weight it gains while grazing on the commons, which in turn depends on the number of goats sent onto the commons, as shown in table below. Assume that if a villager is indifferent between buying a bond and buying a goat, the villager will buy a goat. $$\begin{array} { | c | c | c | } \hline \begin{array} { c } \text { Number of goats } \\\text { on the commons }\end{array} & \begin{array} { c } \text { Price per 2-year } \\\text { old goat } ( \$ ) \end{array} & \begin{array} { c } \text { Income per goat } \\\text { (\$/year) }\end{array} \\\hline 1 & 80 & 30 \\\hline 2 & 75 & 25 \\\hline 3 & 70 & 20 \\\hline 4 & 65 & 15 \\\hline 5 & 55 & 5 \\\hline\end{array}$$ What is the socially optimal number of goats to be sent out onto the commons?

A) 5
B) 4
C) 3
D) 2